A very popular research discipline in control theory is the extension
of control methodologies originally developed for systems that are
described by ordinary differential equations (ODEs) to systems governed
by partial differential equations (PDEs); however, with regard to
stability investigations this extension is accompanied by a significant
rise of complexity, see e.g. [1]} for a comprehensive framework
for the stability analysis of infinite-dimensional systems. Therefore,
a lot of research effort has been invested in this topic, where for
example the stability analysis of mechanical systems with certain
boundary conditions has been addressed. For instance, in [2]}
the stability of an Euler-Bernoulli beam subjected to nonlinear damping
and a nonlinear spring at the tip is analysed, whereas [3]}
is concerned with the stability behaviour of a gantry crane with heavy
chain and payload. Furthermore, the proof of stability of a Lyapunov-based
control law as well as a Lyapunov-based observer design for an in-domain
actuated Euler-Bernoulli beam has been presented in [4]}.
